# What is Quantum information: Definition and 100 Discussions

Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term.
It is an interdisciplinary field that involves quantum mechanics, computer science, information theory, philosophy and cryptography among other fields. Its study is also relevant to disciplines such as cognitive science, psychology and neuroscience. Its main focus is in extracting information from matter at the microscopic scale. Observation in science is one of the most important ways of acquiring information and measurement is required in order to quantify the observation, making this crucial to the scientific method. In quantum mechanics, due to the uncertainty principle, non-commuting observables cannot be precisely measured simultaneously, as an eigenstate in one basis is not an eigenstate in the other basis. As both variables are not simultaneously well defined, a quantum state can never contain definitive information about both variables.Information is something that is encoded in the state of a quantum system, it is physical. While quantum mechanics deals with examining properties of matter at the microscopic level, quantum information science focuses on extracting information from those properties, and quantum computation manipulates and processes information – performs logical operations – using quantum information processing techniques.Quantum information, like classical information, can be processed using digital computers, transmitted from one location to another, manipulated with algorithms, and analyzed with computer science and mathematics. Just like the basic unit of classical information is the bit, quantum information deals with qubits. Quantum information can be measured using Von Neumann entropy.
Recently, the field of quantum computing has become an active research area because of the possibility to disrupt modern computation, communication, and cryptography.

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1. ### Homework Help: Quantum Information Theory 1

I considered an operator ##X \in \mathcal{L}(\mathcal{X} \otimes \mathcal{K})##, that is positive, ##X \geq 0##. And I defined it as it follows: ##X = \sum_{i,j} a_{ij} ∣x_i \rangle \langle x_i ∣ \otimes ∣k_j \rangle \langle k_j∣ ## Where ##x_i## are basis for ##\mathcal{X}## and ##k_j## basis...
2. ### A Fisher information from likelihood function for quantum circuits

In the context of a single phase estimation problem of a quantum photonics experiment. For example consider a 3-photon quantum circuit (such as the Mach-Zehnder which depends on some phase shift operator which encodes a parameter ##\theta##) with a photon counting measurement (two detectors) at...
3. ### I Intersection of Condensed Matter Theory + High Energy Physics

Hey all, I was just wondering where I could find a current review of the major problems that are being discussed at the intersection of condensed matter theory and high energy theory (+maybe quantum information)? Just looking for some inspiration on what the most "popular" problems being...
4. ### Relation between Mutual information and Expectation Values

I've make progress in obtaining the values for the mutual information using the following: $I(\rho_A:\rho_B) = S(\rho_A) +S(\rho_B) - S(\rho_{AB}) = 1 + 1 - 0 = 2.$ I would like to compute the expectation but I'm facing a problem in the case of $\langle\psi |\mathcal{O}_A|\psi \rangle$ since...
5. ### I Is entanglement a consequence of the singularity of the early universe?

Does it make sense to explain entanglement as a consequence of the ‘singularity' of the early universe? If proto matter/energy was in some mathematically definable ’small’ space, perhaps information was likewise compressed, and entanglement is a consequence of this early cosmological locality...
6. ### I On a constructive method of quantum state preparation (Ballentine)

Ballentine, in his Chapter 8.1, appears to give the attached recipe for *in principle* preparing an (almost) arbitrary (pure) state (of a particle with no internal degrees of freedom) by the method of "waiting for decay to the energy ground state". My questions are fourfold: 1) From (8.1), we...
7. ### Quantum Workforce Elements, Toolbox for QIS Programs at Universities

TL;DR Summary: Imagine you have infinite funds and cooperation to build a very ideal curriculum and student organization, both dedicated to quantum information science, at a university. What does this look like pedagogically? How would this be structured? What resources do students need access...
8. ### I Discover Beginner-Friendly Books on Quantum Information and Computation | Q&A

Hello to everyone, I would like to ask you to brief questions. The first one is whether you could recommend any pedagogical books on Quantum Information and Computation. I tried Nielsen and Chuang but I found it too dense for a beginner in the field. The second question is the following: to...
9. ### More Nobel prizes in quantum information?

Alain Aspect, John Clauser & Anton Zeilinger have rightfully received the Nobel prize for their contributions to quantum information, as they were three of the main pioneers of quantum information. However, is it now impossible or very unlikely that other physicists working on this field (e.g...
10. ### I What is the physical meaning of concurence (quantum information)?

Hello, I am currently studying about entanglement on spin-1/2 chains and I was able to find some information about the mathematical point of view of concurrence but I can't understand the physical meaning of it . Can somebody help me, please?
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### Hi，I'm very happy to join this big family for Great Physics

Hi, I'm happy to change ideas in Physics Forums, especially in my interesting fields, include quantum fisher information, and quantum entanglement detection and quantum metrology!

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### How Can Quantum Physics and Econophysics Shape Our Future?

Hello, I am a undergraduate student of physics from nepal. I am passionately curious to understand about the fundamental physical laws of nature. Selectively ,I am interested and passionate to understand quantum physics . I would like to work and research in the field of quantum information...
14. ### A Knill-Laflamme condition Shors code

The K-L condition has projection operators onto the codespace for the error correction code, as I understand it. My confusion I think comes primarily from what exactly these projections are? As in, how would one find these projections for say, the Shor 9-qubit code?
15. ### A Derivation of recovery channel for bit flip error

In general, if R is the recovery channel of an error channel ε, with state ρ, then and according to these lecture slides, we get the final result highlighted in red for a bit flip error channel. I am simply asking how one reaches this final result. Thank you (a full-ish derivation can be found...
16. ### I [Quantum Computing] Quantum Parallelism State Calculation

Hi, I'm going through Nielsen and Chuang's Quantum Computation and Quantum Information textbook and I don't really understand this part about quantum parallelism: Shouldn't the resulting state be (1/sqrt(2^4)) * (|0, f(0)> + |0, f(1)> + |1, f(1)> + |1, f(0)>), since the resulting state would...
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### What is the role of local realism in quantum mechanics?

I studied at UBC, U of Leiden, in quantum statistical mechanics and kinetic theory. I worked in chemistry at McGill University for many years doing the theory of NMR which involves spin theory. In 1997 I gave up NMR and started to study the EPR paradox. I do not follow the party line because I...
18. ### How Can Lagrange Multipliers Determine Maximum Shannon Entropy?

I have used the Lagrange multiplier way of answering. So I have set up the equation with the constraint that ## \sum_{x}^{} p(x) = 1## So I have: ##L(x,\lambda) = - \sum_{x}^{} p(x)log_{2}p(x) - \lambda(\sum_{x}^{} p(x) - 1) = 0## I am now supposed to take the partial derivatives with respect...
19. ### A Suggested reading for quantum information applications in QFT

What would you say is essential reading for those of us who want to understand how exactly is QFT benefiting from QI? Can anyone give a summary of what is happening, and where to start reading? (at postgraduate/entry-research-level).
20. ### A Quantum Ising model correlation function query

In this paper, on quantum Ising model dynamics, they consider the Hamiltonian $$\mathcal{H} = \sum_{j < k} J_{jk} \hat{\sigma}_{j}^{z}\hat{\sigma}_{k}^{z}$$ and the correlation function \mathcal{G} = \langle \mathcal{T}_C(\hat{\sigma}^{a_n}_{j_n}(t_n^*)\cdot\cdot\cdot...
21. ### A Translating/encoding a continuous variable model into a qubit model

I've read these two pages that discuss going from qubit to continuous variable - https://arxiv.org/abs/quant-ph/0008040 and https://arxiv.org/abs/1907.09832 . I'm curious if anyone knows some papers that discuss going the other way around? I.e. qubitizing a continuous variable model? Any insight...
22. ### A Question: Unambiguous discrimination between two non-orthogonal states

Consider a VCSEL laser that emits photon pulses with Poisson distribution for the number of photons per pulse. The power of the VCSEL has been set low so the mean photon number "u" is u<1. Consider this photon pulses can take two non-orthogonal states of polarization (for example: state 0 with...
23. ### A Quantum Information research frontier

I want to pursue research in Quantum Information Theory. I am surveying research topics before applying for PhD in Physics. Can somebody please enlighten me on the latest broad research problems being pursued in Quantum Information?
24. ### How Do Measurements Affect GHZ States?

Here's what I think I understand: First off, the GHZ state ##|GHZ \rangle = \frac {|000\rangle+|111\rangle} {\sqrt 2}##, and ##\sigma_x## and ##\sigma_y## are the usual Pauli matrices, so the four operators are easy to calculate in Matlab. I'm thinking the expectation values of each operator...
25. ### Projective measurements of quantum processor

Am I correct in thinking that the system measures the probability |<f|1>|^2 for some state <f|? Then the probabilities for each of the six states would be: |<0|1>|^2= 0 |<1|1>|^2= 1 |<+x|1>|^2= |(1/√2)|^2 = 1/2 |<-x|1>|^2= |(-1/√2)|^2 = 1/2 |<+y|1>|^2= |(-i/√2)|^2 = 1/2 |<-y|1>|^2= |(i/√2)|^2...
26. ### Qubit Operations: Finding U Gates & Probabilities

Part a: Gate H X Y Z S T R_x R_y Theta pi pi pi pi pi/2 pi/4 pi/2 pi/2 n_alpha (1/sqrt(2))*(1,0,1) (1,0,0) (0,1,0) (0,0,1) (0,0,1) (0,0,1) (1,0,0) (0,1,0) Using the info from the table and equation 1, I find: U_H=(i/sqrt(2))*[1,1;1,-1] U_X=i*[0,1;1,0] U_Y=i*[0,-i;i,0] U_Z=i*[1,0;0,-1]...
27. ### A Expectation Value of a Stabilizer

Given that operator ##S_M##, which consists entirely of ##Y## and ##Z## Pauli operators, is a stabilizer of some graph state ##G## i.e. the eigenvalue equation is given as ##S_MG = G## (eigenvalue ##1##). In the paper 'Graph States as a Resource for Quantum Metrology' (page 3) it states that...
28. ### A Reduced Graph States: Characterizing Basis States

Reduced graph states are characterized as follows from page 46 of this paper: Proposition: Let ##A \subseteq V## be a subset of vertices for a graph ##G = (V,E)## and ##B = V\setminus A## the corresponding complement in ##V##. The reduced state ##\rho_{G}^{A}:= tr_{B}(|G\rangle\langle G|)## is...
29. ### A Conservation of Quantum Information

I can't seem to wrap my head around the notion of conservation of quantum information. One thing that might help that is if someone can tell me what the associated symmetry is. For example, phase symmetry leads to conservation of electric charge according to Noether's theorem; a fact that...
30. ### A Applying General Lorentz Boost to Multipartite Quantum State

I would like to apply a General Lorentz Boost to some Multi-partite Quantum State. I have read several papers (like this) on the theory of boosting quantum states, but I have a hard time applying this theory to concrete examples. Let us take a ##|\Phi^+\rangle## Bell State as an example, and...
31. ### Quantum Quantum information recommendation

I am 3rd year physics student (actually I have just finished it). I have good knowledge on basics of quantum mechanics: I had 1 semester of Introduction to Quantum Physics and then 2 semesters of Quantum Physics. Our literature were Griffiths (Introduction to Quantum Mechanics) and ''Gennaro...
32. ### A Random Quantum Walk: Learn & Use w/ Quantum Gates

I am an undergraduate doing research on QC/QI. My current topic to learn is continuous-time quantum walks, but first I must learn the random quantum walk. That being said, I was wondering if someone could simply explain what a random quantum walk is and then explain how they could be useful with...
33. ### Programs Topics at the junction of AdS/CFT and quantum information

I have been asked to draft a (informal) research proposal for a PhD thesis. I have some background in quantum information and my interests are leaning towards the AdS/CFT correspondence. I was wondering if you could suggest a few (preferably recent) theory papers at the junction of quantum...
34. ### A What is a 'Quantum Coherence'?

I have recently been reading some stuff on quantum information in the physics literature which refers to 'a mechanism by which a measurement in A determines quantum coherences in B', where A and B are subsystems of a larger system. I am aware of the meaning of the terms 'decoherence' and...
35. ### Tensor Product of Hamiltonians

##U_1 \otimes U_2 = (1- i H_1 \ dt) \otimes (1- i H_2 \ dt)## We can write ## | \phi_i(t) > \ = U_i(t) | \phi_i(0)>## where i can be 1 or 2 depending on the subsystem. The ## U ##'s are unitary time evolution operators. Writing as tensor product we get ## |\phi_1 \phi_2> = (1- i H_1 \ dt) |...
36. ### Studying Fields related to Quantum Information

I am a master student in theoretical physics from Italy and I would like to know more about fields related to "Quantum Information". I've been to some seminars and I think that these fields are very interesting, but I need to understand before applying for a PhD. What should I do?
37. ### A How to measure the first qubit in two qubit system? QC

I was wondering how to measure the first or even the second qubit in a quantum computing system after for example a Hadamard Gate is applied to the system of these qubits: A|00>+B|01>+C|10>+D|11>? A mathematical and intuitive explanation would be nice, I am a undergraduate sophomore student...
38. ### Programs Math Major interested in Quantum Information Science

I'm a math major interested in the field of quantum information science and quantum computing, but I'm unclear on what path to take to explore the field. The field is presented as being at the intersection of physics, computer science, and mathematics but it seems that a majority of the experts...
39. ### I How does the thickness of a beam splitter affect the phase shift produced?

I'm having trouble understanding the phase shift produced by a beam splitter. I seem to be finding conflicting information. I'm specifically looking to understand a 50/50 beam splitter where one side has a dielectric mirror, as shown in this figure from wikipedia: I understand the pi...
40. ### Programs Prospects of Pursuing Graduate Studies in Quantum Computing

Hello, I am close to finishing my undergraduate degree in Computer Engineering, and I am very interested in pursuing graduate studies. For a long time, I have been passionate about computer science and I've been looking into the research done in various labs in the schools that I'm considering...
41. ### Finding the magnetization in nuclear magnetic resonance

Homework Statement J-coupling term between two spins is HJ = ħJ/4 σz(1) σz(2) In the measured magnetization spectrum of the spins, this leads to the splitting of the individual spin lines by frequency J, which we’ll now derive. We can write the magnetization of spin 1 as: <M1(t)> =...
42. ### A General quantum measurements

The following, regarding quantum measurement, is stated in the paper "Limitation on the amount of accessible information in a quantum channel" : "Our discussion of measurement will be based on a specific physical model of measurement, to which we now turn. Suppose we have a quantum system ##Q##...
43. ### Physics Is quantum information research well funded?

I am applying to phd programs in physics right now. I am interested in doing research in quantum information science. I see there is a lot of interest and funding for quantum information science right now, but does anyone have any advice on whether or not this research will be well funded in the...
44. ### How do I construct a controlled Hadamard gate?

Homework Statement I am supposed to construct a controlled Hadamard gate using only single qubit and CNOT gates. Homework Equations [/B] We know that any arbitrary unitary Operator U can be written as the Martrix product U=AXBXC, where X is the NOT-Matrix and ABC=1 (identity matrix) I've...
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### Physics Orienting myself toward quantum computing or a related field

I am well aware that QC-related graduate programs are competitive so I am preparing myself for a rejection. Not because I'm unconfident. But because everyone should have a backup plan just in case. I haven't applied yet because I'm about to take the GRE. I really do enjoy both quantum physics...
47. ### Other Quantum Information and General Relativity

Last year I've finished the undergraduate course in Mathematical-Physics and Mathematics and this year I've started on graduate school on Physics in order to obtain a master's degree. What I'm really interested are two main topics: general relativity and quantum field theory. I also like...
48. ### Schools Top Graduate Schools for Quantum Information and Computing

Hey all! I'm a junior undergrad and am beginning to think about what graduate programs I would like to apply to next fall. Recently I've been doing theoretical research in quantum computing which I'm really enjoying. I'm pretty sure that this is the sort of research I would like to pursue in...
49. ### A H-theorem in quantum information theory

An interesting paper has appeared on nature.com: http://www.nature.com/articles/srep32815 The abstract: I expect this to spawn plenty of pop science claims about "scientists say we can reverse entropy". But the paper itself looks like a good discussion of how the second law actually works...
50. ### Programs Where can I do a masters in Quantum Mechanics?

I am an undergraduate student in India doing my final year BS degree in Math. I am extremely interested in quantum mechanics and want to peruse quantum computation. What is the best possible course that I can take for my Masters? There appears to be a limited number of colleges that offer a...